#ifndef VEC3_H
#define VEC3_H
#include <cmath>
#include <iostream>
using std::sqrt;

class vec3 {
  public:
    double e[3];
    vec3(): e{0, 0, 0} {}
    vec3(double e0, double e1, double e2):e{e0, e1, e2} {}

    double x() const {return e[0];}
    double y() const {return e[1];}
    double z() const {return e[2];}

    vec3 operator-() const {return vec3(-e[0], -e[1], -e[2]);}
    double operator[](int index) const {return e[index];}
    double &operator[](int index) {return e[index];}

    vec3& operator+=(const vec3& v) {
      e[0] += v.e[0];
      e[1] += v.e[1];
      e[2] += v.e[2];
      return *this;
    }

    vec3& operator*=(double t) {
      e[0] *= t;
      e[1] *= t;
      e[2] *= t;
      return *this;
    }

    vec3& operator/=(double t) {
      return *this *= 1 / t;
    }

    double length() const {
      return sqrt(length_sequared());
    }

    double length_sequared() const {
      return e[0] * e[0] + e[1] * e[1] + e[2] * e[2];
    }
};

using point3 = vec3;

inline std::ostream& operator<<(std::ostream& out, const vec3& v) {
  return out << v.e[0] << ' ' << v.e[1] << ' ' << v.e[2];
}

inline vec3 operator+(const vec3& u, const vec3& v) {
  return vec3(u.e[0] + v.e[0], u.e[1] + v.e[1], u.e[2] + v.e[2]);
}

inline vec3 operator-(const vec3& u, const vec3& v) {
  return vec3(u.e[0] - v.e[0], u.e[1] - v.e[1], u.e[2] - v.e[2]);
}

inline vec3 operator*(const vec3& u, const vec3& v) {
  return vec3(u.e[0] * v.e[0], u.e[1] * v.e[1], u.e[2] * v.e[2]);
}
// TODO:
#endif // VEC3_H
